gam - How can I implement random smooth with common trajectory and different scale in R mgcv package?

Question

I am trying to implement a special case of generalized additive mixed model using R mgcv package without success and in need of advice.

Specifically, the model has mixed effect of levels which scales common smooth link function (please see the attached figure). In other words, the model has random smooth with common trajectory (curvature) but differently scaled.

I have already tried

gam(y ~ te(level,x,bs=c('re','tp'),k=3))

where level denotes a factor variable denoting levels with mixed effects, and x denotes a continuous variable. But this results in smooth link function with different trajectory.

Thank you in advance.

Answer 1

等待大神答复